7.1a Mean

7.1a Mean
1. The mean of the data is an average value obtained by using the formula:

(A) Ungrouped Data

Example 1
(a) Find the mean for the set of data 2, 4, 7, 10, 13, 16 and 18.

(b) A value of x is added into the above set of data, the mean for
this new data is 9.5. Determine the value of x.

Solution:
(a)
$\begin{array}{l}\overline{x}=\frac{2+4+7+10+13+16+18}{7}\\ \overline{x}=\frac{70}{7}=10\end{array}$
(b)

(B) Grouped Data (Without Class Interval)

Example 2
The frequency table shows the marks obtained by 40 students in a Biology test.

 Marks 50 55 60 65 70 Number of students 6 8 15 10 1

Find the mean marks.
Solution:

(C) Grouped Data (With Class Interval)

Example 3
The grouped frequency distribution was obtained from 100 students regarding the scores in their test shown as below.

 Scores Frequency 5 – 9 4 10 – 14 10 15 – 19 19 20 – 24 26 25 – 29 21 30 – 34 12 35 – 39 8
Find the mean scores.

Solution:

 Scores Frequency f Midpoint x fx 5 – 9 4 7 28 10 – 14 10 12 120 15 – 19 19 17 323 20 – 24 26 22 572 25 – 29 21 27 567 30 – 34 12 32 384 35 – 39 8 37 296 Total 100 2290